Supported by a wealth of learning features, exercises, and visual elements as well as online video tutorials and interactive simulations, this book is the first student-focused introduction to Bayesian statistics.

Without sacrificing technical integrity for the sake of simplicity, the author draws upon accessible, student-friendly language to provide approachable instruction perfectly aimed at statistics and Bayesian newcomers. Through a logical structure that introduces and builds upon key concepts in a gradual way and slowly acclimatizes students to using R and Stan software, the book covers:

An introduction to probability and Bayesian inference

Understanding Bayes' rule

Nuts and bolts of Bayesian analytic methods

Computational Bayes and real-world Bayesian analysis

Regression analysis and hierarchical methods

This unique guide will help students develop the statistical confidence and skills to put the Bayesian formula into practice, from the basic concepts of statistical inference to complex applications of analyses.

Chapter 1: How to best use this book

The purpose of this book

Who is this book for?

Pre-requisites

Book outline

Route planner - suggested journeys through Bayesland

Video

Problem sets

Code

R and Stan

Why don’t more people use Bayesian statistics?

What are the tangible (non-academic) benefits of Bayesian statistics?

Part I: An introduction to Bayesian inference

Chapter 2: The subjective worlds of Frequentist and Bayesian statistics

Bayes’ rule - allowing us to go from the effect back to its cause

The purpose of statistical inference

The world according to Frequentists

The world according to Bayesians

Do parameters actually exist and have a point value?

Frequentist and Bayesian inference

Bayesian inference via Bayes’ rule

Implicit versus Explicit subjectivity

Chapter 3: Probability - the nuts and bolts of Bayesian inference

Probability distributions: helping us explicitly state our ignorance

Independence

Central Limit Theorems

A derivation of Bayes’ rule

The Bayesian inference process from the Bayesian formula

Part II: Understanding the Bayesian formula

Chapter 4: Likelihoods

What is a likelihood?

Why use ‘likelihood’ rather than ‘probability’?

What are models and why do we need them?

How to choose an appropriate likelihood?

Exchangeability vs random sampling

Maximum likelihood - a short introduction

Chapter 5: Priors

What are priors, and what do they represent?

The explicit subjectivity of priors

Combining a prior and likelihood to form a posterior

Constructing priors

A strong model is less sensitive to prior choice

Chapter 6: The devil’s in the denominator

An introduction to the denominator

The difficulty with the denominator

How to dispense with the difficulty: Bayesian computation

Chapter 7: The posterior - the goal of Bayesian inference

Expressing parameter uncertainty in posteriors

Bayesian statistics: updating our pre-data uncertainty

The intuition behind Bayes’ rule for inference

Point parameter estimates

Intervals of uncertainty

From posterior to predictions by sampling

Part III: Analytic Bayesian methods

Chapter 8: An introduction to distributions for the mathematically-un-inclined

The interrelation among distributions

Sampling distributions for likelihoods

Prior distributions

How to choose a likelihood

Table of common likelihoods, their uses, and reasonable priors

Distributions of distributions, and mixtures - link to website, and relevance

Supplements

An excellent resource on Bayesian analysis accessible to students from a diverse range of statistical backgrounds and interests. Easy to follow with well documented examples to illustrate key concepts.

Bronwyn Loong

College of Business and Economics, Australian National University

When I was a grad student, Bayesian statistics was restricted to those with the mathematical fortitude to plough through source literature. Thanks to Lambert, we now have something we can give to the modern generation of nascent data scientists as a first course. Love the supporting videos, too!

Wray Buntine

Information Technology, Monash University

Written in highly accessible language, this bookis the gateway for students to gain a deep understanding of the logic of Bayesian analysis and to apply that logic with numerous carefully selected hands-on examples. Lambert moves seamlessly from a traditional Bayesian approach (using analytic methods) that serves to solidify fundamental concepts, to a modern Bayesian approach (using computational sampling methods) that endows students with the powerful and practical powers of application. I would recommend this book and its accompanying materials to any students or researchers who wish to learn and actually do Bayesian modeling.

Fred Oswald

Psychology, Rice University

A balanced combination of theory, application and implementation of Bayesian statistics in a not very technical language. A tangible introduction to intangible concepts of Bayesian statistics for beginners.

Golnaz Shahtahmassebi

Senior Lecturer in Statistics, School of Science & Technology, Nottingham Trent University

The late, famous statistician Jimmie Savage would have taken great pleasure in this book based on his work in the 1960s on Bayesian statistics. He would have marveled at the presentations in the book of many new and strong statistical and computer analyses.

Gudmund R. Iversen

Professor Emeritus of Statistics, Swarthmore College

While there is increasing interest in Bayesian statistics among scholars of different social science disciplines, I always looked for a text book which is accessible to a wide range of students who do not necessarily have extended knowledge of statistics. Now, I believe that this is the first textbook of Bayesian statistics, which can also be used for social science undergraduate students. Ben Lambert begins with a general introduction to statistical inference and successfully brings the readers to more specific and practical aspects of Bayesian inference. In addition to its well-considered structure, many graphical presentations and reasonable examples contribute for a broader audience to obtain well-founded understanding of Bayesian statistics.

Susumu Shikano

Political Methodology, Centre for Data and Methods, University of Konstanz

This book offers a path to get into the field of Bayesian statistics with no previous knowledge. Building from elementary to advanced topics, including theoretic and computational aspects, and focusing on the application, it is an excellent read for newcomers to the Bayesian world.

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